About the size of a 50p, including legspan? The Twitter photo looks much more like a Steatoda grossa, a native false widow species. I have them around my home but rarely see them. I wouldn't be concerned. Possibly relocate any wandering males you might find, but they are quite reclusive.

A cave spider (Meta menardi) can grow much bigger and is more inclined to shuffle off out of the light to a hiding place.